Question

The position vectors of the vertices A, B and C of a tetrahedron ABCD are i + j + k,i and 3i, respectively. The altitude from vertex D to the opposite face ABC meets the median line through A of the triangle ABC at a point E. If the length of the side AD is 4 and the volume of the tetrahedron is 2√2/2, find the position vector of the point E for all its possible positions.

Answer 1

Let E divides AF in λ :1. The position vector of E is given by

and when λ  = - 2,position vector of E is given by,